Snapping vertices in a particle system
With some inspiration from this answered question, though some settings must have been changed because I can't find the other size determining value, he pointed out, I managed to find the right Render>size "0.25" which makes the particles the same size as the original Dupli Object and takes the selected polar vertices to the same spot as I wanted. 

and to do the eventual How to convert particles to mesh? 
and How to Make Multi User Objects Single User?
is required